Answer: 0.0995
Step-by-step explanation:
The cumulative distribution function for exponential distribution for random variable x is given by :-
[tex]F(x)=1-e^{-\lambda x}[/tex], where [tex]\lambda[/tex] is the mean of the distribution .
Given : The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 30 days.
Then [tex]\lambda=\dfrac{1}{30}[/tex]
[tex]P(x<18)=1-e^{-\frac{1}{30}\times18}\approx0.4512[/tex]
[tex]P(x<24)=1-e^{-\frac{1}{30}\times24}\approx0.5507[/tex]
Now, the probability that the time between two unplanned shutdowns is between 18 and 24 days will be :-
[tex]P(x<24)-P(x<18)=0.5507-0.4512=0.0995[/tex]
Hence, the probability that the time between two unplanned shutdowns is between 18 and 24 days =0.0995
